The Present Value Formula
A dollar today is worth more than a dollar in the future. That's not just intuition — it's mathematics. Money available now can be invested and grow, so a future payment is always worth less than its face value in today's terms. Present value is the calculation that quantifies exactly how much less.
The Formula
Present value is the reverse of future value. If the future value formula tells you what a sum grows to, the present value formula tells you what a future sum is worth right now:
$$P = \frac{F}{(1 + r)^t}$$
- \(P\) = present value (today's equivalent)
- \(F\) = future value (the amount you'll receive later)
- \(r\) = annual discount rate as a decimal
- \(t\) = number of years
The discount rate is whatever rate of return you could reasonably expect if you had the money today — often an interest rate, investment return, or inflation rate depending on the context.
Example 1
You're promised $20,000 in 4 years. If money earns 6% annually, what is that payment worth today?
$$P = \frac{20000}{(1.06)^4} = \frac{20000}{1.2625} \approx $15,842$$
You'd need to invest $15,842 today at 6% to have $20,000 in four years — so that's what the future promise is worth now.
Example 2
You'll receive $50,000 in 20 years. Assuming 3% annual inflation, what is that payment worth in today's dollars?
$$P = \frac{50000}{(1.03)^{20}} = \frac{50000}{1.8061} \approx $27,684$$
Even though the check will say $50,000, it will only buy what $27,684 buys today. Inflation acts as the discount rate here.
Present Value Calculator
Practice Problems
1. What is the present value of $5,000 to be received in 8 years, discounted at 4%? Show answer\(P = \frac{5000}{(1.04)^8} = \frac{5000}{1.3686} \approx $3,655\).
2. You win a prize of $100,000 to be paid in 10 years. If you could invest at 7% annually, what would you accept as a lump sum today instead? Show answer\(P = \frac{100000}{(1.07)^{10}} = \frac{100000}{1.9672} \approx $50,835\). Any lump sum above this is worth more than waiting 10 years.
3. Two options: receive $8,000 today or $10,000 in 5 years. If your discount rate is 5%, which is better? Show answerPresent value of $10,000 in 5 years: \(\frac{10000}{(1.05)^5} \approx $7,835\). That's less than $8,000 today, so take the $8,000 now.